Question: Simplify the following expression: $a = \dfrac{-9z^2 - 108z - 315}{z + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ a =\dfrac{-9(z^2 + 12z + 35)}{z + 7} $ Then we factor the remaining polynomial: $z^2 + {12}z + {35} $ ${7} + {5} = {12}$ ${7} \times {5} = {35}$ $ (z + {7}) (z + {5}) $ This gives us a factored expression: $\dfrac{-9(z + {7}) (z + {5})}{z + 7}$ We can divide the numerator and denominator by $(z - 7)$ on condition that $z \neq -7$ Therefore $a = -9(z + 5); z \neq -7$